Quantum Cats

The quantum world has long since been one of those seemingly incomprehensible sources of wonder and awe. So infinitesimally small, yet so significant. This article is dedicated to my favourite quantum animal (which also happens to be the only quantum animal I’m aware of ): Schrodinger’s cat.

Note: This article has been adapted from one of my high school technical reports for a physics project, as a result of which much of the language is… technical.

Austrian physicist, Erwin Schrodinger, arguably owned the most famous cat of the twentieth century, second only to Garfield. Popularised by his famous hypothetical experiment, this feline, has become the subject of extensive research over the last century, and continues to be a much debated topic in the realm of quantum physics, till date.

The sticky quantum situation

In the light of Neils Bohr and Werner Heisenberg’s work, the world could be described to exist separately, yet simultaneously, as a macrocosm and microcosm. In the macrocosm, Newtonian mechanics and the laws of classical physics were sufficient to describe physical phenomena as we knew it. However, the microcosm presented a completely different scenario.

Bohr’s theory, proposed that electrons circle the nucleus following the classical laws (Newtonian mechanics) but subject to certain limitations, such as the orbits they can occupy and the energy they lose as radiation during transition from one orbit to another. However, it also attempted to explain all the quantum phenomena that had been observed till then, in a unified way. It was formulated based upon the adiabatic principle and the correspondence principle.

Heisenberg’s uncertainty principle stated that the position and momentum of a particle cannot be measured simultaneously with absolute precision. In other words, the more accurately one of these two values is known, the less we know about the other value.

For quite a while, physicists had followed the Copenhagen interpretation of quantum mechanics, which stated that a quantum system would remain in a superposition until observed by an external entity. The limitation here, was that such a system’s existence was restricted to the microcosm.

Around this time, Max Born came up with a way to deal with the prevailing problem on the conflicting nature of particles and waves. He formulated a new kind of probability, completely independent of the Maxwell-Boltzmann theory of averages (used in the kinetic theory of gases). The wave Ψ (‘psi’) could then be understood as the probability of finding an electron in a particular position. Ψ had no physical significance as it was the probability amplitude of a quantum superposition. The time finally came, when an attempt was made to establish a link between Born’s findings and the prevailing Copenhagen interpretation.

A tale of two kitties

Schrodinger’s cat was first mentioned in his paper, ‘The Present Situation in Quantum Mechanics’ written during a correspondence with Albert Einstein in October, 1935, on the EPR article. The article primarily discussed the extraordinary nature of photons and subatomic particles to exist in multiple states simultaneously, shaking the very foundations of atomic ontology and epistemology as had been known till then. Einstein’s explanation employed an unstable keg of gunpowder which, over a period of time, could exist in an exploded and unexploded state.

Schrodinger, followed this up by extending the theory to a macroscopic entity: his cat.

“A cat is penned up in a steel chamber, along with a Geiger counter, which must be secured against direct interference by the cat. The Geiger counter contains a small amount of radioactive substance, which is so small that perhaps in the course of an hour, one of the atoms decays, but also with equal probability, perhaps none. If an atom decays, the counter tube discharges and – through a relay – releases a hammer that shatters a small flask of hydrocyanic acid. But if no atom decays after an hour, the cat still lives. The ψ (‘psi’) function of the entire system would express this by having in it, the living and dead cat mixed in equal parts.”

Thus as long as the chamber remained closed to the outside world, the cat would exist in a quantum superposition, being 50% alive and 50% dead simultaneously. Upon being viewed by an external observer, however, the quantum superposition would collapse into a definite state of being: Either wholly alive, or entirely dead. In this case, a particle released by the nuclear decay of the radioactive source acts as a quantum event. After a period of time, it could have decayed and not decayed, causing the flask to be broken and intact, resulting in the cat being both, dead and alive. It was from here that the idea of a quantum event encapsulating macroscopic entities by virtue of cause and effect, first cropped up.

Max Born’s interpretation of ψ as the probability amplitude of the wave-function, also implied that while the quantum superposition used two wave functions, its decoherence would result in a single wave function. Although Schrodinger proposed the experiment to ridicule the possibility of using probability to interpret his wave function, Born’s view of Schrodinger’s paradoxical cat is still used to teach the concepts of quantum probability and the superposition of quantum states.

This is a classical perspective of the experiment where 1 indicates a definite positive outcome and 0 indicates a negative outcome (as seen by external observer):

CAT IS ALIVE

CAT IS DEAD

NUCLEAR DECAY OCCURS

0

1

NUCLEAR DECAY DOES NOT OCCUR

1

0

Quantum perspective of the experiment where 1/2 indicates 50% probability of either of the two possible states (as Schrodinger’s hypothesis suggests):

CAT IS ALIVE

CAT IS DEAD

NUCLEAR DECAY OCCURS

1/2

1/2

NUCLEAR DECAY DOES NOT OCCUR

1/2

1/2

What does the cat observe?

To answer this question, it is necessary to first ensure that our assumption of the quantum system involves nothing beyond the physical boundaries of this experimental setup. Theoretically, we could say that the cat itself lives in a state of limbo, never actually seeing the outcome of the quantum event. This, however, does not imply that it is unable to observe the event from within, but simply that its conscious observation will always remain in the outcome where there is the greatest probability of it being alive. In other words, the cat perpetually remains alive in 50% of all possible outcomes. There would always be at least one outcome wherein the cat is definitely alive.

This could well be seen as a way for it to live forever, but the moment it attempts to free itself from the confinement of the box, it will break the quantum superposition by causing the external (classical) world to observe it, thus resulting in a definite decoherence of its wave function. Whether or not, it remains alive after that, is entirely a matter of chance, governed by a 100% randomly triggered nuclear decay.

Yet another question one may ask, is how the state of the emitted particle from the radioactive source could possibly link itself with the cat’s ontology.

The term used to describe such a phenomena is now known as quantum entanglement. New laboratory research has shown that such a phenomena is indeed possible between two particles with opposite quantum spins. In an entangled pair of particles, the first particle has a quantum spin in a given direction (say up); now, the other particle will definitely spin down. Even when these two particles are separated, their unique property of entanglement will cause each to have the opposite spin of the other.

A similar property could be used to determine the state of the cat.

The cat’s state could be either dead or alive. Let’s assume that dead corresponds to 0 and alive corresponds to 1. Let’s also assume that the occurrence of a radioactive emission corresponds to 1 and its non-occurrence corresponds to 0.

Hence, the cat, by virtue of being entangled with the particle’s state, is alive (1) only when the particle is not emitted (0), and it is dead only when the particle is emitted (1).

Foraying into the quantum realm

Schrodinger’s cat, although no more than a thought-experiment given little importance in his day, has opened up a multitude of opportunities in the field of quantum physics. Technology for faster communication systems and more powerful processors running on ‘qubits’ (quantum bits), rather than regular bits, is currently underway. The world record for information processing through quantum entanglement, achieved in April 2018, was an 18-qubit Greenberger-Horne-Zeilinger entanglement system with six photons, exploiting three degrees of freedom on each one (including path, polarisation and angular momentum).

Quantum computing will undoubtedly be the next major scientific revolution, completely changing the way humanity perceives the microscopic world.

Such computers use a completely different architecture from classical processing units. They utilise quantum bits (qubits) which can exist in multiple states in order to perform mathematical calculations at far greater speeds, compared to conventional bits. Such qubits, are used in pairs, on pairs of particles like photons, to perform operations and measure the results (within experimental error). As of July 2018, a simulation by Lloyd Hollenberg’s team at the Pawsey Supercomputing Centre (in Perth, Western Australia), broke the world record for quantum computing by using Shor’s algorithm (a quantum algorithm to find the prime factors of extremely large integers) demonstrating how the first quantum computers could perform in real world scenarios.

As John Archibald Wheeler (Emeritus Professor of Physics at Princeton University) once said after proposing the title: ‘The Quantum: The Glory and the Shame’:

“Why glory? Because there is not a branch of physics which the quantum does not illuminate. The shame, because we still do not know “how come the quantum?””.

John Archibald Wheeler

At the end of the day, what fascinated me the most, was that in the entire process of developing quantum theory, from over a century ago, to present day, across the range of arguments proposed all over Europe by its pioneers, just one animal had an entire experiment dedicated to it: Schrodinger’s cat.

Bibliography:

Parsons, Paul. How to Destroy the Universe: and 34 Other Really Interesting Uses of Physics. Quercus, 2011.

Abrams, Iwona, et al. Great Theories of Science: Three Brilliant Graphic Guides on Mind-Blowing Ideas That Have Revolutionised Our View of How the Universe Works. Icon, 2013.